ERIC ED458132: Patterns, Functions, and Algebra: Wired for Space. NASA Connect: Program 3 in the 2000-2001 Series.

29 Pages·2000·0.7 MB·English

by  ERIC

DOCUMENT RESUME
SE 065 303
ED 458 132
Patterns, Functions, and Algebra: Wired for Space. NASA
TITLE
Connect: Program 3 in the 2000-2001 Series.
National Aeronautics and Space Administration, Hampton, VA.
INSTITUTION
Langley Research Center.
EG-2000-10-17-LaRC
REPORT NO
2000-00-00
PUB DATE
28p.; Accompanying videotape not available from ERIC.
For
NOTE
other documents in series, see SE 065 301-305.
Teacher (052)
Classroom
Guides
PUB TYPE
MF01/PCO2 Plus Postage.
EDRS PRICE
*Algebra; *Electricity; *Functions (Mathematics); Integrated
DESCRIPTORS
Activities; Intermediate Grades; Junior High Schools;
*Magnets; Mathematics Education; *Patterns in Mathematics;
Science and Society; Science Instruction; Space Sciences;
Technology Education
*Spacecraft
IDENTIFIERS
ABSTRACT
This teaching unit is designed to help students in grades 5
to 8 explore the concepts of patterns, functions, and algebra in the context
of propelling spacecraft. The units in the series have been developed to
enhance and enrich mathematics, science, and technology education and to
accommodate different teaching and learning styles. Each unit consists of
background notes for the teacher, a list of teacher resources, and two
activities, one of which is Web-based, complete with blackline masters. Also
included are suggestions for extensions to the problems and their
relationships to national mathematics, science, and technology standards. In
this activity, students learn how patterns, functions, and algebra can help
National Aeronautics and Space Administration (NASA) engineers design new
ways of propelling spacecraft and how electricity and magnetism are being
used to replace the fuel-consuming rocket propulsion commonly used to deliver
a push to spacecraft.
(MM)
Reproductions supplied by EDRS are the best that can be made
from the original document.
A
A
Patterns, Functions,
and Algebra:
Wired for Space
U S DEPARTMENT OF EDUCATION
Office of Educational Research and Improvement
EDUCATIONAL RESOURCES INFORMATION
CENTER (ERIC)
1..
document has been reproduced as
.lits
received from the person or organization
originating it
0 Minor changes have been made to
improve reproduction quality
Points of view or opinions stated in this
document do not necessarily represent
official OERI position or policy
01
ProVaat Iheerview
Classroom Activity
Student Cue Cards p. 2,3
p.24
Web Activity
esourteS
Educator's Guide
P-25
Teachers &
Students
This publication is in the PublDomain and is not protected by copyright. Permission is not required for duplication .
Publication Number EG-2000-10-17-LaRC
prc-r rnpy
ARI P
Program 3 in the 2000-2001 NASA CONNECT Series
Patterns, Functions, and Algebra: Wired for Space
PROGRAM OVERVIEW
SUMMARY AND OBJECTIVES
In Patterns, Functions, and Algebra: Wired for Space, students will learn how
patterns, functions, and algebra can help NASA engineers design new ways of
propelling spacecraft and how electricity and magnetism are being used to replace
the fuel-consuming rocket propulsion commonly used to deliver a push to
spacecraft. Students will discover three projects that use electromagnetism in a
dynamic way: the Magnetic Levitation Launch System (Maglev), the Propulsive
Small Expendable Deployer System (ProSEDS), and the student-designed Icarus
satellite. Students will observe NASA engineers using algebra to design and test
the Icarus satellite. Through classroom and on-line activities, students will make
connections between electricity and magnetism and between NASA research and
the mathematics, science, and technology they learn in their classroom.
INTERACTIVE ACTIVITIES
Questions are posed throughout the video by Norbert, the animated cohost of
NASA CONNECT. These questions direct the instruction and encourage students to
think about the concepts being presented. An icon appears in the video to suggest
to teachers an appropriate 'place to pause the video and discuss the answers to the
questions. Students record their answers on the Student Cue Cards (p. 23).
The hands-on Classroom Activity (p. 2), entitled Make it Go!, is classroom-tested
and aligned with the National Council of Teachers of Mathematics standards, the
National Science Education standards, and the International Technology Education
Association standards for technological literacy. Students will construct, operate,
and collect data from a device that demonstrates electrodynamic propulsion. They
will explore how the amount of current flowing through a wire coil affects its
deflection in a magnetic field. This activity provides an opportunity for students to
gather and then discuss complicated data in terms of broad, sweeping trends. See
Figure 1. Overview of EDU setup.
Figure 1, an illustration of the electrodynamic demonstrator unit (EDU).
The coil moves when the circuit is
closed. Students investigate how the
The on-line activity, entitled the Internet Plasma Physics Education eXperience
current level affects this motion.
(IPPEX), is aligned with the National Council of Teachers of Mathematics standards,
(For enlarged view, see p. 16.)
the National Science Education standards, and the National Educational Technology
standards. This activity invites students to explore basic concepts involved with
electricity and magnetism, such as static charge, moving charge, voltage, resistance,
and current. IPPEX is located in Norbert's lab at
http://connect.larc.nasa.gov/wired/lab.html.
z RESOURCES
Teacher and student resources (pp. 25 and 26) support, enhance, and extend the
NASA CONNECT program. Books, periodicals, pamphlets, and web sites provide
teachers and students with background information and extensions. In addition to
the resources listed in this lesson guide, the NASA CONNECT web site
http://connectiarc.nasa.gov offers on-line resources for teachers, students, and
parents. Teachers who would like to get the most from the NASA CONNECT web
site can access Norbert's Lab and receive assistance from the Lab Manager.
Program 3 in the 2000-2001 NASA CONNECT Series
Patterns, Functions, and Algebra: Wired for Space
THE CLASSROOM ACTIVITY
BAcKGROUND
Make it Go! is designed to demonstrate the same force that NASA will use in its
propellant-free satellite propulsion system, to be tested in the ProSEDS mission.
Unlike MagLev, which offers the promise of providing lower cost and safer launches
by replacing much of the rocket fuel needed to get spacecraft into orbit, ProSEDS
would be employed once the spacecraft reaches orbit.
High-speed Maglev trains use magnetism to lift the train body off the tracks, causing
them to ride not on the tracks but through the air. Once the vehicle is off the tracks,
electromagnets are arranged so that the magnetism pushes the train forward. Magnetism
dramatically reduces frictional forces and the use of energy required to overcome them.
More energy can be used to propel the vehicle forwardand fast! Adapted to spacecraft,
MagLev could be used in the first phase of a launch to boost the spacecraft upward along
an inclined track. Once the spacecraft reaches a critical speed, rockets would take over and
provide the final push required to send the vehicle into orbit.
Typically, an orbiting spacecraft expends propellants (fuels) to direct its motion.
Propellants help push the vehicle into higher orbit or force it to leave orbit quickly
once the craft is out of service. When replacing these fuels, the ProSEDS system
employs a long, electrically conducting wire tethered to a spacecraft. The Earth's
magnetic field, which extends into the zone in which satellites orbit the Earth, will
give a magnetic push to this current-carrying tether. The tether will transfer this force
to the spacecraft, making it move. Soon, ProSEDS technology will be tested on a
satellite called Icarus. The object of the test will be to examine how well ProSEDS
will work to rapidly force the satellite out of orbit (to burn up in Earth's atmosphere).
The satellite is named Icarus after the tragic Greek mythological character who fell to
Earth while trying to fly too close to the Sun with waxen wings.
Students will work in small teams to construct a device, make observations, and
collect data on how different levels of current affect the distance that the coil moves.
The objectives of the activity are to (1) provide students with a concrete example of
the technology presented in the NASA CONNECT video, (2) provide an opportunity
for students to explore the relationship between electric current and the movement
of a coil in a magnetic field, and (3) discuss the phenomenon in terms of broad
patterns or trends that are both qualitative and quantitative. Through their
explorations, students make predictions, test them, take measurements, and discuss
and graph patterns.
As a project that will expand your students' math competencies, the activity helps
develop their ability to think about patterns and trends in the way two variables
relate to one another, with consideration of qualitative observations, quantitative
data relating to these observations, and the visualization of these data in the form
of a graphall of which support and develop the basic pattern or trend that relates
current levels in the circuit to the distance the coil moves.
While the ability to recognize and "see" an overall trend is an important precursor to
more formal understandings of the concepts of linear and nonlinear functions, this
unit was not designed to provide a formal, concrete introduction to functions; the
nature of the relationship between the magnet and the current in the coil is too
complex to provide a simple introduction to functions.
Program 3 in the 2000-2001 NASA CONNECT Series
Patterns, Functions, and Algebra: Wired for Space
NATIONAL STANDARDS
MATHEMATICS STANDARDS
Understand patterns, relations, and functions.
Use mathematical models to represent and understand quantitative relationships.
Analyze change in various contexts.
Understand measurable attributes of objects and the units, systems, and
processes of measurement.
Apply appropriate techniques, tools, and formulas to determine measurement.
Formulate questions that can be addressed with data and collect, organize, and
display relevant data to answer them.
Develop and evaluate inferences and predictions that are based on data.
Recognize and apply mathematics in contexts outside mathematics.
Use representations to model and interpret physical, social, and mathematical
phenomena.
SCIENCE STANDARDS
Abilities necessary to do scientific inquiry
Understandings about scientific inquiry
Motions and forces
Transfer of energy
TECHNOLOGY STANDARDS
Various relationships exist between technology and other fields of study.
Throughout history, innovations in technology have resulted from the demands,
values, and interests of individuals, businesses, industry, and societies.
The process of experimentation, which is common in science, can also be used to
solve technological problems.
Some technological problems are best solved through experimentation.
Follow step-by-step directions to assemble a product.
5
Program 3 in the 2000-2001 NASA CONNECT Series
Patterns, Functions, and Algebra: Wired for Space
INSTRUCTIONAL OBJECTIVES
Students will be able to
construct an electrodynamic demonstrator unit (EDU).
use the EDU to observe that changing the current in a circuit affects the light
emitted from an LED (light emitting diode).
observe and understand that a wire with electricity flowing through it can be
made to move in the presence of a magnet.
observe that changing the current in a circuit affects the amount of movement
induced in the electric wire when a magnetic field is present.
measure, record, and graph the relationship between the electric current and the
wire movement.
discuss general trends in the data.
VOCABULARY
Here are some terms that are used throughout this activity with which your students
may not be familiar. You may want to spend some time developing their
understandings'of the relevant concepts.
current
the flow of electrons or charged particles in an electric circuit
force
a push or a pull on an object
electrodynamic
related to the interactions of electric currents with magnetic fields
electromagnetic
related to electricity and magnetism
trend
a general pattern of how a system behaves, relating two or more variables
to one another
6
Program 3 in the 2000-2001 NASA CONNECT Series
Patterns, Functions, and Algebra: Wired for Space
PREI)ARING FOR TiIE ACTIVITY
MATERIALS
For items that may be difficult to find, Radio Shack part numbers and pricing
information are included.*NASA does not endorse Radio Shack as a supplier
of materials; these materials can be replaced with parts from other suppliers, as well.
FOR ENTIRE CLASS
wire cutters
scissors
PER STUDENT TEAM (2-3 STUDENTS)
1 tall, sturdy box (at least 30 cm high, 15 cm wide, and 30 cm deep), with magnet
hole prepared (See instructions for preparing the magnet hole in the Advance
Preparation section of this guide, p.6.)
1 piece of corrugated cardboard about 15 cm x 30 cm (approximately the size of
the box top) to serve as a platform for the batteries, LED, and Current Controller.
Electrical resistors in the following sizes:
Used in Extension activity
Required for Basic activity
33 ohm
22 ohm
47 ohm
82 ohm
68 ohm
220 ohm
100 ohm
470 ohm
150 ohm
1000 (1K) ohm
330 ohm
All these resistors may be obtained from Radio Shack in packets of 5 for 49/.
roll of magnet wire (30 or 32 AWG), with enamel coating
1
(Radio Shack offers a magnet wire 3-pack: 40 ft of 22 gauge, 75 ft of 26 gauge,
and 200 ft of 30 gauge wire. Part number 278-1345; $3.99)
alligator clip leads (small toothed)
(Radio Shack sells 14 in. length, double-headed alligator clip leads. Part number
278-1156; package of 10, $3.99)
24 in. length, double-headed alligator clip leads
(Radio Shack: Part number 278-1157; package of 8, $3.99)
2 fresh D cell batteries
battery holder for two D-cells (for D-cells with wires/leads attached)
(Radio Shack: Part number 270-386; $1.59)
1 LED (light emitting diode)
(Radio Shack provides an LED assortment: Part number.276-1622; package of 20, $2.29)
tape (cellophane or masking)
fine sandpaper for removing enamel insulation from magnet wire
1 Current Controller, prepared by teacher ahead of time (See instructions on
Current Controller Templates, Figure 5, p. 20.)
strip of manila folder, 3 cm x 16 cm (prepared ahead of time by teacher)
toothpick
mm ruler
film can (container for 35-mm film; available free to teachers at most film
developing establishments)
cow magnet (available through science education supply catalogues)
*The use of trademarks or names of manufacturers in this report is for accurate reporting and does not
constitute an official endorsement, either expressed or implied, of such products or manufacturers by the
National Aeronautics and Space Administration.
7
Program 3 in the 2000-2001 NASA CONNECT Series
Patterns, Functions, and Algebra: Wired for Space
TIME
Overall, this activity will take four 45-minute sessions.
Introduce and demonstrate teacher's EDU and build student EDUs with LED (steps
1 and 2): 90 min (two 45-min sessions).
Add coil and magnet to EDU and observe, measure, graph, and interpret the effects
of varying levels of electric current (steps 4 through 5): 90 minutes (two 45-min
sessions).
ADVANCE PREPARATION
1. Construct and become familiar with the behavior of the electrodynamic
demonstration unit (EDU) (see enlarged view of Figure 1, p. 16). Student Work
Sheets 1 and 2 (pp. 13-15) provide instructions for building the EDU.
2. Once you have built the EDU, try all the suggested activities before you conduct
Figure 1. (as seen on p. 1)
the lesson and demonstrate a completed EDU to the entire class. The initial
Overview of EDU Setup.
demonstration to the class is done without the magnet and coil in place, so
(For enlarged view, see
remove them before demonstrating the model.
Figure 1, p.16.)
3. Prepare 3-cm x 16-cm manila folder strips (1 per student team)
Level 1
4. Prepare one Current Controllers (Figure la, p. 6) for each student team,
according to the instructions on the Current Controller Template (Figure 5, p. 20).
Level 2
5. Cut magnet holes in boxes. Each hole should be on the front, vertical face of lie
Level 4
EDU, 2-1/2 cm from the right edge and about 20 cm from the top of the box.
NOTE: Making this hole can be a little tricky, so we recommend you try it on another
Level 8
box or another part of the box before cutting the "real" hole. The important thing is
that the magnet be held in the hole firmly and perpendicular to the box. One good way
Level 16
is to make a hole slightly smaller than the magnet and then push the magnet into that
hole.
Figure la.
Front view of completed
CAUTION: The LED can be damaged by excess current running through it.
CAUTION
Current Controller.
To limit the current and avoid such damage, always use the current
(For instructions, see
regulator in the circuits that you connect
Figure 5, p. 20.)
NOTE: The LED has polarity It operates only when the current flows through it in a
specific direction. Make sure that the negative lead from the battery holder is connected
to the shorter lead on the LED. (The leads are the small metal "legs" sticking out from
the bottom of the LED.) If the LED does not work, try reversing the leads. That_should
take care of the problem.
Figures in the Activity
Figurel
..
p. 16
Overview of EDU Setup
Figure 2.
p. 17
EDU Circuit with Cod
.
Figure 1
p. 18
EDU Circuit Without Coil
.
Figure 4,
Coil Mounted on
p 19
Manilla Fokier
8
Figure 5
Current Controller
p 20
Templates
0
Program 3 in the 2000-2001 NASA CONNECt Series
Patterns, Functions, and Algebra: Wired for Space
THE ACTIVITY
STEP 1: INTRODUCE AND DEMONSTRATE THE MODEL (THE EDU)
A. INTRODUCE THE ACTIVITY
1. Begin this activity with the idea that you will be exploring the same effect that
NASA is hoping to use to propel satellites in spaceelectrodynamic propulsion.
Also introduce the idea that the way you will be exploring this effect is to look
for patterns and trends in how the effect acts. Point out that scientists and
engineers explore such patterns in their work. Math is a useful tool that helps us
examine and describe patterns and trends.
2. Arrange students so that everyone can get a good look at your electrodynamic
demonstration unit (EDU). Ask them to describe it. Explain that you have set
up one continuous circuit that connects batteries, a bulb (LED), and a long,
Is the circuit on? How can students tell? As a
continuous coil to one another.
class, trace the (would-be) path of electricity, identifying where there is no
connection.
3. Relate the EDU to NASAs electrodynamic propulsion system (featured in the
NASA CONNECT video). Point out that the device you are working with is a good
model of NASA's ProSEDS mission. NASA will make electricity run through the
long wire tether, represented by the coiled wire:The Earth's magnetic field is
represented by the cow magnet (see Figure 1, p. 16). The magnetism acts on the
current and makes the wire move, just as the tether and satellite will move in
Earth's weaker, but larger magnetic field.
B. DEMONSTRATE THE CIRCUIT (WITHOUT THE COIL)
NOTE: For this part of the activity, keep the Current Controller setting at Level 16the
greatest current. You may wish to dim the room lights so that the LED light is more visible.
This step establishes a common understanding of the circuit. You also have a chance to
introduce a familiar phenomenonthe generation of light upon the closure of a
circuitas an indicator that current is flowing. The lit LED will serve as an indicator of
flowing current throughout the rest of this activity.
1. Tell students you want to look only at the LED for now, so you are going to take
the coil out of the circuit. Close the EDU circuit in a way that bypasses the coil.
Ask students to share their observations of what happens. (The LED will light,
showing that there is a continuous, electrically conducting path.)
2. As a class, trace the path of electricity through the circuit to verify that the circuit
is closed.
3. Show and describe the purpose of the Current Controller to students, taking note
of the relationship between the current levels. (The purpose of the Current
Controller is to allow students to set the current to very specific levels. A higher
current level setting corresponds to a greater amount of current in the circuit. The
levels are set so that increasing the setting from one level to the next highest one
results in a doublingapproximately of the amount of current. Thus, Level 4
provides twice as much current as Level 2.)
4. Ask students to think about and predict what will happen to the LED when the
circuit is set at the different current levels. Record the predictions on the board,
emphasizing that students are making qualitative predictions about how the
current level and the illumination of the.LED relate. (Groups of students may have
a variety of opposing opinions. They may say nothing will change or that the LED
will shine more brightly with greater or with lower current levels.)
9
Program 3 in the 2000-2001 NASA CONNECT Series
Patterns, Functions, and Algebra: Wired for Space
5. Do not change the current level on your model. Instead, challenge student teams
to build their own EDUs and test their predictions.
STEP 2: BUILD EDUs WITHOUT COILS OR MAGNETS
NOTE: This step allows students to experience firsthand the EDU circuit and the Current
Controller They can verify for themselves that changing the levels on the Current
Controller actually changes the current flowing in the circuit. The LED serves as an
indicator of the amount of current flowing in the circuit. In Step 3, they build the coil
and add it, along with the magnet, to,the EDU.
A. BUILD EDU CIRCUIT WITHOUT COILS OR MAGNETS
1. Distribute Student Worksheet 1
(p. 13) to each team of 2-3 students and
distribute the materials listed.
2. Discuss the construction steps before students begin building their EDUs.
3. Circulate among the groups and help them construct their EDUs.
B. EXPLORE EDU AND LED
1. Encourage students to explore how the brightness of the LED changes as the
current level changes.
2. Circulate among the working groups to encourage careful and systematic
observations.
C. DISCUSS STUDENT OBSERVATIONS AS A CLASS
1. Compare student observations to their predictions.
2. Challenge students to make one (or more) statements about the relationship they
observe between the current level and the illumination of the LED. Is there a
general trend to this relationship?
3. Emphasize that the trend we observe holds true as the current levels get higher
or lower. The light from the LED gets brighter or dimmer with higher or lower
current levels. Some trend statements might be "The higher the current, the
brighter the LED lights," or "The lower the current, the less brightly the LED
lights."
4. Ask students to predict what they would observe if the current level were set at
a level between the ones they have availablefor example, how brightly would
the LED shine at Level 10? (Not as brightly as at Level 16, but brighter than at
Level 8.)
STEP 3: ADDING COIL AND MAGNET TO THE EDU
1. Distribute Student Worksheet 2 (pp. 14 and 15) and the materials listed.
2. Instruct students to keep the circuit open until they test the circuit. Remind them
to maintain the current level setting at 16.
CAUTION: Remind students that they may damage the LED beyond repair
if they do not include the Current Controller in the circuit.
NOTE: You may wish to stop all activity once students have assembled the EDU with the
coil and the magnet to instruct the whole class about the next steps. However, if your
students can work independently, the activity will flow more smoothly if you allow
teams to move on their own through the rest of Step 3 and all of Step 4, as soon as the
coils, magnets, and rulers are added to the EDU. You can facilitate this activity by
circulating around the room and instructing the teams as they are ready to move on.